Finite Group Databasebeta

← #29584172

Subgroups — #29584172

Order 15616.

342 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21445993C211yesmaximal, characteristic
2#21444549C212yesmaximal
3#21444434C212yesmaximal
4#21443730C211yesmaximal, characteristic
5C61×#3255C211yesmaximal, characteristic
6#16839819C2212yes—
7C2×#14519712—22no—
8#16839786C2211yescharacteristic
9C2×#14519688C2211yescharacteristic
10#16839511—22no—
11#16839508—22no—
12#16839504—24no—
13C61×#533C2212yes—
14C61×#475—22no—
15C61×#470—22no—
16C61×#462—22no—
17C61×#423C2211yescharacteristic
18C2×#11758194—21no—
19C22×#92418—21no—
20#14519712—44no—
21C4⋊#92418—22no—
22C4⋊#92418—22no—
23C22⋊#92418—22no—
24#14519688—21no—
25#14519688—22no—
26#14519688D412yes—
27C2×Q16×C61—22no—
28C2×M16×C61D412yes—
29C4⋊Q8×C61D412yes—
30C4⋊Q8×C61D412yes—
31#125×C61—22no—
32C22⋊Q8×C61—22no—
33C22⋊Q8×C61—22no—
34C4×Q8×C61—22no—
35C4×Q8×C61—22no—
36#117×C61—22no—
37C2×C42×C61C2311yescharacteristic
38#106×C61—22no—
39C4⋊C8×C61—22no—
40#103×C61—24no—
41C2×Q8×C61—22no—
42C2×Q8×C61—22no—
43C22×C4×C61C2×D411yescharacteristic
44C22×C4×C61#4112yes—
45Q16×C61—82no—
46M16×C61—42no—
47C2×C8×C61—22no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61—22no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61—22no—
52C4⋊C4×C61—42no—
53C4⋊C4×C61—42no—
54C22⋊C4×C61—42no—
55C42×C61—42no—
56C42×C61C2×D412yes—
57C42×C61C2×D411yescharacteristic
58C42×C61#4111yescharacteristic
59#11758194—42no—
60C2×#92418—22no—
61C2×#92418—22no—
62C2×#92418—22no—
63C2×#92418—41no—
64C2×#92418—42no—
65C23×C61#12411yescharacteristic
66Q8×C61—42no—
67Q8×C61—42no—
68Q8×C61—82no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—42no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61#12011yescharacteristic
75C2×C4×C61#12111yescharacteristic
76C2×C4×C61#12112yes—
77C2×C4×C61#12312yes—
78C8×C61—42no—
79#92418—24no—
80#92418—82no—
81#92418—81no—
82#10528—611nomaximal, Sylow
83C22×C61—22no—
84C22×C61—21no—
85C22×C61#39411yescharacteristic
86C4×C61—22no—
87C4×C61—22no—
88C4×C61—21no—
89C4×C61—82no—
90C4×C61—82no—
91C4×C61#45311yescharacteristic
92C4×C61#45611yescharacteristic
93#3255D6111yescharacteristic
94#1849—611no—
95#1559—612no—
96#1531—612no—
97#1307—611no—
98C2×C61—41no—
99C2×C61#203911yescharacteristic
100C2×C61#204912yes—
101#533C2×D6112yes—
102#475—22no—
103#470—22no—
104#462—22no—
105#432—612no—
106C2×#108—1222no—
107#423—611no—
108#423C2×D6111yescharacteristic
109C2×#97—611no—
110#333—1222no—
111#332—1222no—
112#330—1224no—
113C61#1052811yescharacteristic, complemented, Sylow
114C2×Q16—22no—
115C2×M16—1221no—
116C2×M16C22⋊D6112yes—
117C22×C8—1221no—
118C4⋊Q8C22⋊D6112yes—
119C4⋊Q8C22⋊D6112yes—
120#125—22no—
121C22⋊Q8—22no—
122C22⋊Q8—22no—
123C4×Q8—22no—
124C4×Q8—22no—
125#117—22no—
126C2×C42C22×D6111yescharacteristic
127#108—2444no—
128#106—22no—
129C4⋊C8—22no—
130C4⋊C8—1222no—
131C4⋊C8—1222no—
132#103—24no—
133C22⋊C8—1222no—
134#97—612no—
135#97—1222no—
136#97—1221no—
137C2×Q8—22no—
138C2×Q8—22no—
139C22×C4#1175822412yes—
140C22×C4C2×C22⋊D6111yescharacteristic
141Q16—82no—
142M16—42no—
143M16—2442no—
144C2×C8—22no—
145C2×C8—1222no—
146C2×C8—1222no—
147C2×C8—1222no—
148C2×C8—2441no—
149C2×C8—2442no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C22⋊C4—42no—
157C42—42no—
158C42D4×D6111yescharacteristic
159C42#1175822411yescharacteristic
160C42C2×C22⋊D6112yes—
161C23#1451976411yescharacteristic
162Q8—42no—
163Q8—42no—
164Q8—82no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4#1451974611yescharacteristic
171C2×C4#1451974811yescharacteristic
172C2×C4#1451974912yes—
173C2×C4#1451975812yes—
174C8—42no—
175C8—1224no—
176C8—4882no—
177C8—4881no—
178C22—21no—
179C22—22no—
180C22#1683967611yescharacteristic
181C4—21no—
182C4—22no—
183C4—22no—
184C4—82no—
185C4—82no—
186C4#1683993011yescharacteristic
187C4#1683994511yescharacteristic
188C2—41no—
189C2#2144704011yescharacteristic
190C2#2144709612yes—
subgroupG/H
centerC22#16839676
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3255C2
socleC22×C61#394
prime radicalC23×C61#124
hypercenter#3255D61
hypocenterC61#10528
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3255

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
113. C61#10528semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214459932
#214445492
#214444342
#214437302
C61×#32552
#1052861